Network architecture and spatio-temporally symmetric dynamics (2008)
We examine the relation between the structure of a network and the spatio-temporally symmetric periodic dynamics it can support. If we are looking for solutions in which no cell is stationary, then...
Network architecture and spatio-temporally symmetric dynamics (2008)
We examine the relation between the structure of a network and the spatio-temporally symmetric periodic dynamics it can support. For solutions in which no cell is stationary, we show that only...
SYMMETRY AND PATTERN FORMATION ON THE VISUAL CORTEX (2008)
Martin Golubitsky, Liejune Shiau, Andrei Török
Mathematical studies of drug induced geometric visual hallucinations include three components: a model that abstracts the structure of the primary visual cortex V1; a mathematical procedure for...
Abstract. Let f: X → X be the restriction to a hyperbolic basic set of a smooth diffeomorphism. We find several criteria for transitivity of noncompact connected Lie group extensions. As a...
coboundary equation on Cantor sets (2008)
We prove Whitney regularity results for the solutions of the coboundary equation over dynamically defined Cantor sets satisfying a natural geometric regularity condition, in particular hyperbolic...
On the Cohomology of Anosov Actions (2008)
Viorel Nitica, Andrei Török, Andrei Trk
The goal of this survey is to present recent cohomological results in the theory of Anosov actions, as well as to show how they are related to other results in the eld. Due to constraints of space,...
Nonabelian Cohomology of Abelian Anosov Actions (2007)
Anatole Katok, Viorel Nitica, Andrei Török
.We develop a new technique for calculating the first cohomology of certain classes of actions of higher--rank abelian groups (Z k and R k , k 2) with values in a linear Lie group. In this paper we...
An Open Dense Set Of Stably Ergodic Diffeomorphisms In A Neighborhood Of A Non-Ergodic One (2007)
. As a special case of our results we prove the following. Let A 2 Diff r (M) be an Anosov diffeomorphism. Then there is a C r -neighborhood of A \Theta Id S 1 that contains an open dense set of...
Abstract. We prove certain rigidity properties of higher-rank abelian product actions of the type α × IdN: Z κ → Diff(M × N),whereα is (TNS) (i.e. is hyperbolic and has some special structure...
Patterns of synchrony in coupled cell networks with multiple arrows (2005)
Martin Golubitsky, Ian Stewart, Andrei Török
Abstract. A coupled cell system is a network of dynamical systems, or “cells, ” coupled together. The architecture of a coupled cell network is a graph that indicates how cells are coupled and...
Whitney regularity for solutions to the coboundary equation on Cantor sets (2005)
We prove Whitney regularity results for the solutions of the coboundary equation over dynamically defined Cantor sets satisfying a natural geometric regularity condition, in particular hyperbolic...
Statistical Limit theorems for suspension flows (2004)
In dynamical systems theory, a standard method for passing from discrete time to continuous time is to construct the suspension flow under a roof function. In this paper, we give conditions under...
Variable Step Random Walks and Self-Similar Distributions ∗ (2004)
Gemunu H. Gunaratne, Joseph L. Mccauley, Matthew Nicol, Andrei Török
We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit...
Michael Field, Ian Melbourne, Andrei Török
Abstract. We obtain sharp results for the genericity and stability of transitivity, ergodicity and mixing for compact connected Lie group extensions over a hyperbolic basic set of a C 2...
Statistical Limit Theorems for Suspension Flows (2004)
In dynamical systems theory, a standard method for passing from discrete time to continuous time is to construct the suspension flow under a roof function.
Rigidity Of Partially Hyperbolic Actions Of Property (t) Groups (2003)
We show that volume-preserving perturbations of some product actions of property (T) groups exhibit a "foliation rigidity" property, which reduces the partially hyperbolic action to a...
Central Limit Theorems and Invariance Principles for Time-One Maps of Hyperbolic Flows (2002)
We give a general method for deducing statistical limit laws in situations where rapid decay of correlations has been established. As an application of this method, we obtain new results for time-one...
Local Rigidity of Certain Partially Hyperbolic Actions of Product Type (2001)
. We prove certain rigidity properties of higher--rank abelian product actions of the type ff \Theta IdN : Z ! Diff(M \Theta N), where ff is (TNS) (i.e., is hyperbolic and has some special structure...
Non-abelian cohomology of abelian Anosov actions (2000)
Anatole Katok, Viorel Nitica, Andrei Török
We develop a new technique for calculating the first cohomology of certain classes of actions of higher-rank abelian groups (Z , k 2) with values in a linear Lie group. In this paper we consider the...
Regularity Of The Transfer Map For Cohomologous Cocycles (1998)
Viorel Nitica, Andrei Torok, Viorel Ni ¸tică, Andrei Török
In this paper we obtain results about the regularity of the transfer map between two cocycles over an Anosov system, with values in either a diffeomorphism or a Lie group. We also explain how certain...
Viorel Nitica, Andrei Török, X. Introduction, The Main Result
this paper we obtain regularity results for the Livsic cohomology equation for cocycles with values in dieomorphism and Lie groups
This paper emerges from an attempt to understand the dierentiable actions close to 0 . After Zimmer initiated the program to classify volume-preserving actions of higher rank lattices on compact...